Generalized Integral Transform Method for the Bending Analysis of Clamped Rectangular Thin Plates

The article presents Generalized Integral Transform Method (GITM) for the bending analysis of clamped rectangular thin plates. The problem is a boundary value problem (BVP) represented by a fourth order partial differential equation (PDE). Linear combinations of product of eigenfunctions of vibrating clamped thin beams in the in-plane dimensions are used to formulate the sought for deflection function w(x, y) in terms of a double series with unknown generalized deflection parameters cmn. The GITM converts the BVP to an integral equation and ultimately to an algebraic problem in terms of cmn, which is solved to fully obtain ( , ) w x y as a double infinite series found to be convergent. Bending moments are obtained using the bending moment deflection relations as double infinite series with convergent properties. The solutions obtained for deflection and bending moments at the center and middle of the clamped edges for the two considered cases of uniformly distributed load and hydrostatic load are in agreement with previous results in literature. The effectiveness of the GITM for the clamped plate problem is thus illustrated.